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During the recent experiments and PIC simulations, quasi-monoenergetic for electron is observed [1, 2]. Forming the free of cold plasma electrons cavity behind the laser pulse is possible instead of periodic plasma wave and plasma channel guided method [3]. In this bubble cavity a dense bunch of relativistic electrons with a monoenergetic spectrum is self-generated [3].The profiles [3] and PIC simulation [4] show the ellipsoid shape cavity behind the laser pulse. In this work we present an analytical ellipsoid model and discuss how quasi-monoenergetic electron is produced in the bubble field  

Using the ellipsoidal cavity model, the quasi-monoenergetic electron output beam in laser-plasma interaction is described. By the cavity regime the quality of electron beam is improved in comparison with those generated from other methods such as periodic plasma wave field, spheroidal cavity regime and plasma channel guided acceleration. Trajectory of electron motion is described as hyperbolic, parabolic or elliptic paths. We find that the self-generated electron bunch has a smaller energy width and more effective gain in energy spectrum. Initial condition for the ellipsoidal cavity is determined by laser-plasma parameters. The electron trajectory is influenced by its position, energy and...